hw6_lshen.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Q1.\n",
    "\n",
    "Add a __setitem__ to the python linked list implementation from the lecture (this past wednesday)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#your code here\n",
    "from doctest import run_docstring_examples as dtest\n",
    "import numbers\n",
    "import reprlib\n",
    "class LL:\n",
    "    \"\"\"\n",
    "    >>> A = LL()  \n",
    "    >>> A[0]\n",
    "    Traceback (most recent call last):\n",
    "        ...\n",
    "    IndexError: trying to index an empty LL\n",
    "    >>> A.insert_front(1)\n",
    "    >>> A[0]\n",
    "    1\n",
    "    >>> A.insert_back(2)\n",
    "    >>> A[1]\n",
    "    2\n",
    "    >>> A\n",
    "    LL([1,...])\n",
    "    >>> myll = LL.from_components([1,2])\n",
    "    >>> myll[1]\n",
    "    1\n",
    "    >>> len(myll)\n",
    "    2\n",
    "    >>> myll[2]\n",
    "    Traceback (most recent call last):\n",
    "        ...\n",
    "    IndexError: LL index out of range\n",
    "    >>> myll[0:1]\n",
    "    Traceback (most recent call last):\n",
    "        ...\n",
    "    TypeError: LL indices must be integers\n",
    "    >>> myll= LL.from_components([1,2,3,4,5])\n",
    "    >>> myll[2]=999\n",
    "    >>> print(myll[2])\n",
    "    \"\"\"    \n",
    "    @classmethod\n",
    "    def from_components(cls, components):\n",
    "        inst = cls(components[0])\n",
    "        for c in components[1:]:\n",
    "            inst.insert_front(c)\n",
    "        return inst\n",
    "        \n",
    "    def __init__(self, head=None):\n",
    "        if head is None:\n",
    "            self._headNode = None\n",
    "        else:\n",
    "            self._headNode = [head, None]\n",
    "            \n",
    "    def insert_front(self, element):\n",
    "        new_node = [element, None]\n",
    "        new_node[1] = self._headNode\n",
    "        self._headNode = new_node\n",
    "        \n",
    "    def insert_back(self, element):\n",
    "        new_node = [element, None]\n",
    "        curr_ptr = self._headNode\n",
    "        while curr_ptr[1] is not None:\n",
    "            curr_ptr = curr_ptr[1]\n",
    "        curr_ptr[1]= new_node\n",
    "        \n",
    "    def __repr__(self):\n",
    "        class_name = type(self).__name__\n",
    "        if len(self)==0:\n",
    "            components=\"\"\n",
    "        else:\n",
    "            components = reprlib.repr(self[0])\n",
    "        return '{}([{},...])'.format(class_name,components)\n",
    "\n",
    "\n",
    "    def __len__(self):\n",
    "        curr_ptr = self._headNode\n",
    "        count = 0\n",
    "        if curr_ptr==None:\n",
    "            return 0\n",
    "        while 1:\n",
    "            count = count + 1\n",
    "            if curr_ptr[1] is None:\n",
    "                break\n",
    "            curr_ptr = curr_ptr[1]\n",
    "        return count    \n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        class_name = type(self).__name__\n",
    "        if isinstance(index, numbers.Integral): \n",
    "            curr_ptr = self._headNode\n",
    "            if curr_ptr==None:\n",
    "                msg = 'trying to index an empty {class_name}' \n",
    "                raise IndexError(msg.format(class_name=class_name))\n",
    "            next_ptr = self._headNode[1]\n",
    "            count = 0\n",
    "            while 1:\n",
    "                if index == count:\n",
    "                    return curr_ptr[0]\n",
    "                if curr_ptr[1] is None:\n",
    "                    msg = '{class_name} index out of range' \n",
    "                    raise IndexError(msg.format(class_name=class_name))       \n",
    "                count += 1\n",
    "                curr_ptr = curr_ptr[1]\n",
    "        else:\n",
    "            msg = '{class_name} indices must be integers' \n",
    "            raise TypeError(msg.format(class_name=class_name))\n",
    "\n",
    "    def __setitem__(self, index, value):\n",
    "        '''\n",
    "        If class is empty, return an error.        \n",
    "        Index must be an integer.\n",
    "        '''\n",
    "        class_name = type(self).__name__\n",
    "        if isinstance(index, numbers.Integral): \n",
    "            curr_ptr = self._headNode\n",
    "            \n",
    "            if curr_ptr==None:\n",
    "                msg = 'trying to set an value to an empty {class_name}' \n",
    "                raise IndexError(msg.format(class_name=class_name))\n",
    "            count = 0\n",
    "            \n",
    "            while 1:\n",
    "                if index == count:\n",
    "                    curr_ptr[0]=value  \n",
    "                    break\n",
    "                if curr_ptr[1] is None:\n",
    "                    msg = '{class_name} index out of range' \n",
    "                    raise IndexError(msg.format(class_name=class_name))       \n",
    "                count += 1\n",
    "                curr_ptr = curr_ptr[1]                \n",
    "        else:\n",
    "            msg = '{class_name} indices must be integers' \n",
    "            raise TypeError(msg.format(class_name=class_name))   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n",
      "1\n",
      "2\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "A = LL() \n",
    "A.insert_front(1)\n",
    "A.insert_back(2)\n",
    "A.insert_back(6)\n",
    "A.insert_front(8)\n",
    "for i in range(len(A)):\n",
    "    print(A[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n",
      "1\n",
      "9999\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "A[2]=9999\n",
    "for i in range(len(A)):\n",
    "    print(A[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q2.\n",
    "\n",
    "An online mean and standard deviation algorithm.\n",
    "\n",
    "Below is a function to generate a potentially infinite stream of 1-D data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from random import normalvariate, random\n",
    "from itertools import count\n",
    "def make_data(m, stop=None):\n",
    "    for _ in count():\n",
    "        if stop and _ > stop:\n",
    "            break\n",
    "        yield 1.0e09 + normalvariate(0, m*random() )\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an implementation of an online mean algorithm..see http://www.johndcook.com/blog/standard_deviation/ and the link to http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/ in-between. (Convince yourselves of the formulas...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def online_mean(iterator):\n",
    "    n = 0\n",
    "    mu = 0\n",
    "    for value in iterator:\n",
    "        n += 1\n",
    "        delta = value - mu\n",
    "        mu = mu + delta/n\n",
    "        yield mu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use out generator functions to implement iterators:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1000000006.3887864,\n",
       " 1000000000.5286058,\n",
       " 999999999.7417309,\n",
       " 1000000002.332919,\n",
       " 1000000002.1701045,\n",
       " 999999999.6515665,\n",
       " 1000000000.5676593,\n",
       " 999999997.4282551,\n",
       " 1000000000.8693393,\n",
       " 1000000003.9877218,\n",
       " 1000000004.2908862]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = make_data(5, 10)\n",
    "list(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'generator'>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[999999999.526433,\n",
       " 1000000000.3641977,\n",
       " 1000000000.4810851,\n",
       " 999999999.9797695,\n",
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       " 1000000000.5106837,\n",
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       " 999999999.7653942,\n",
       " 999999999.8243897,\n",
       " 1000000000.1831175,\n",
       " 1000000000.0571306,\n",
       " 1000000000.052187,\n",
       " 999999999.5983552,\n",
       " 999999999.5615196,\n",
       " 999999999.5710664,\n",
       " 999999999.5483329,\n",
       " 999999999.5060202,\n",
       " 999999999.3190868,\n",
       " 999999999.4205573,\n",
       " 999999999.5408367,\n",
       " 999999999.571825,\n",
       " 999999999.6366389,\n",
       " 999999999.6427875,\n",
       " 999999999.6816021,\n",
       " 999999999.721305,\n",
       " 999999999.7657585,\n",
       " 999999999.7026886,\n",
       " 999999999.80346,\n",
       " 999999999.6948384,\n",
       " 999999999.7025276,\n",
       " 999999999.8259987,\n",
       " 1000000000.0257204,\n",
       " 1000000000.0651122,\n",
       " 1000000000.0098832,\n",
       " 999999999.9970167,\n",
       " 999999999.9786587,\n",
       " 999999999.926443,\n",
       " 999999999.9965507,\n",
       " 999999999.9919745,\n",
       " 999999999.9087212,\n",
       " 999999999.9681408,\n",
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       " 999999999.8607315,\n",
       " 999999999.8909817,\n",
       " 999999999.7893529,\n",
       " 999999999.7433481,\n",
       " 999999999.7614489,\n",
       " 999999999.7246604,\n",
       " 999999999.7798127,\n",
       " 999999999.7787604,\n",
       " 999999999.7936205,\n",
       " 999999999.6098739,\n",
       " 999999999.5618533,\n",
       " 999999999.5446911,\n",
       " 999999999.5783857,\n",
       " 999999999.5831156,\n",
       " 999999999.5858346,\n",
       " 999999999.535236,\n",
       " 999999999.561183,\n",
       " 999999999.6028098,\n",
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       " 999999999.6477404,\n",
       " 999999999.6277975,\n",
       " 999999999.6195583,\n",
       " 999999999.6169298,\n",
       " 999999999.6331508,\n",
       " 999999999.6382604,\n",
       " 999999999.5951445,\n",
       " 999999999.618052,\n",
       " 999999999.6081107,\n",
       " 999999999.5985446,\n",
       " 999999999.6457396,\n",
       " 999999999.6527867,\n",
       " 999999999.6809772,\n",
       " 999999999.6800213,\n",
       " 999999999.6563348,\n",
       " 999999999.6604308,\n",
       " 999999999.652322,\n",
       " 999999999.6731383,\n",
       " 999999999.6771872,\n",
       " 999999999.6842455,\n",
       " 999999999.6890765,\n",
       " 999999999.7041869,\n",
       " 999999999.6738334,\n",
       " 999999999.64924,\n",
       " 999999999.653472,\n",
       " 999999999.6596264]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = online_mean(make_data(5, 100))\n",
    "print(type(g))\n",
    "list(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1\n",
    "\n",
    "Implement the standard deviation algorithm as a generator function as\n",
    "\n",
    "```python\n",
    "def online_mean_dev(iterator):\n",
    "    BLA BLA\n",
    "    if n > 1:\n",
    "        stddev = math.sqrt(dev_accum/(n-1))\n",
    "        yield (n, value, mu, stddev)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# your code here\n",
    "import math\n",
    "def online_mean_dev(iterator):    \n",
    "    '''\n",
    "    This function calculates the running mean and stdev from \n",
    "    http://www.johndcook.com/blog/standard_deviation/\n",
    "    Input: An iterator\n",
    "    Output\n",
    "    n: Sample length\n",
    "    value: current value\n",
    "    mu: mean\n",
    "    stddev: standard deviation \n",
    "    \n",
    "    Examples:\n",
    "    online_mean_dev(range(10000))\n",
    "    '''\n",
    "    n=0    \n",
    "    for value in iterator:\n",
    "        n=n+1        \n",
    "        if n==1:\n",
    "            mu=value\n",
    "            dev_accum=0        \n",
    "        else:    \n",
    "            mu_new=mu+(value-mu)/n\n",
    "            dev_accum=dev_accum+(value-mu)*(value-mu_new)\n",
    "            mu=mu_new            \n",
    "        if n > 1:\n",
    "            stddev = math.sqrt(dev_accum/(n-1))\n",
    "            yield (n, value, mu, stddev)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we make 100000 element data, and run this iterator on it (imagine running this on a time-series being slowly read from disk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data_with_stats = online_mean_dev(make_data(5, 100000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       " (997, 1000000000.1415957, 1000000000.0767968, 2.92205704292017),\n",
       " (998, 1000000000.864803, 1000000000.0775864, 2.920697767741369),\n",
       " (999, 1000000008.3024622, 1000000000.0858195, 2.930809474968793),\n",
       " (1000, 999999999.9228221, 1000000000.0856565, 2.9293467709189205),\n",
       " (1001, 999999998.9941207, 1000000000.0845661, 2.9280849871524106),\n",
       " ...]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(data_with_stats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q3.\n",
    "\n",
    "Let's do Anomaly detection. Write a routine `is_ok`:\n",
    "\n",
    "```python\n",
    "def is_ok(level, t)\n",
    "```\n",
    "\n",
    "which takes a tuple like the one yielded by your code above and returns True if the value is inbetween `level`-$\\sigma$ of the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#your code here\n",
    "def is_ok(level, t):\n",
    "    '''\n",
    "    This function tes if the current value is inbetween `level`-$\\sigma$ of the mean\n",
    "    Input \n",
    "    level: one real number\n",
    "    t: one tuple returned by online_mean_dev function\n",
    "    \n",
    "    Output\n",
    "    It returns True if the value is inbetween `level`-$\\sigma$ of the mean\n",
    "    \n",
    "    Examples:\n",
    "    t=(60560, 1000000016.82255, 1000000000.0108689, 2.8986933335015728)\n",
    "    is_ok(5,t)\n",
    "    '''    \n",
    "    std=t[3]\n",
    "    avg=t[2]\n",
    "    if abs(t[1]-avg)<=level*std:\n",
    "        return True\n",
    "    else:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use this function to create a predicate passed through to `itertools.filterfalse` which is then used to obtain an iterator on the anomalies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data_with_stats = online_mean_dev(make_data(5, 100000))\n",
    "from itertools import filterfalse\n",
    "pred = lambda t: is_ok(5, t)\n",
    "anomalies = filterfalse(pred, data_with_stats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We materialize the anomalies..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1767, 999999981.1999818, 999999999.9481188, 2.9679021045256375),\n",
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       " (15995, 1000000015.9688977, 999999999.9852803, 2.8971159648753666),\n",
       " (16720, 1000000016.2427914, 999999999.9853187, 2.9050077769884592),\n",
       " (16981, 1000000014.6017127, 999999999.9824498, 2.909780255583098),\n",
       " (18632, 999999985.161428, 999999999.9785969, 2.9104031832401756),\n",
       " (18829, 1000000018.5245534, 999999999.9786646, 2.915138462548738),\n",
       " (22374, 1000000021.9375612, 999999999.9825976, 2.909150473756884),\n",
       " (27093, 999999983.786455, 999999999.9854801, 2.9002936244161677),\n",
       " (29794, 999999985.2076782, 999999999.9873073, 2.894771179173713),\n",
       " (32162, 999999984.928268, 999999999.98238, 2.9014394938331094),\n",
       " (33943, 999999984.1279236, 999999999.9780501, 2.8954646326792797),\n",
       " (38535, 999999984.2955364, 999999999.9755945, 2.9015687051542853),\n",
       " (42432, 1000000014.6169283, 999999999.9772787, 2.8923972029493266),\n",
       " (43355, 1000000016.7721993, 999999999.9776729, 2.891512683031122),\n",
       " (47066, 1000000018.2696077, 999999999.9749213, 2.8899702049315317),\n",
       " (48946, 1000000017.3144059, 999999999.977395, 2.8907340523189617),\n",
       " (51172, 999999983.7676924, 999999999.977887, 2.890287665942597),\n",
       " (54966, 1000000014.7581389, 999999999.9805489, 2.8879663053313025),\n",
       " (65951, 1000000014.6934221, 999999999.9846874, 2.883199489520228),\n",
       " (69799, 999999984.0197047, 999999999.9845396, 2.883528593504261),\n",
       " (70699, 999999983.860995, 999999999.9850887, 2.882964804176591),\n",
       " (72710, 1000000018.0631969, 999999999.9843836, 2.8882340099908337),\n",
       " (72837, 999999984.2647856, 999999999.9841784, 2.889203519427726),\n",
       " (74638, 1000000014.8409437, 999999999.9870484, 2.8902285787294386),\n",
       " (76357, 999999982.9956977, 999999999.9880236, 2.8912237132135052),\n",
       " (76524, 1000000014.4527364, 999999999.9883256, 2.8920054406709506),\n",
       " (78244, 999999983.6581821, 999999999.9895614, 2.891162625867402),\n",
       " (81459, 999999984.5761648, 999999999.9879936, 2.887135650549175),\n",
       " (82188, 999999984.9188826, 999999999.988925, 2.8876536713767678),\n",
       " (82614, 1000000014.9316325, 999999999.9886621, 2.8885676786492795),\n",
       " (89552, 1000000015.3214945, 999999999.987791, 2.88974664533084),\n",
       " (94219, 999999984.8802755, 999999999.9880875, 2.8901366371526325),\n",
       " (96973, 1000000016.1604058, 999999999.9885015, 2.891204329091082),\n",
       " (97572, 1000000014.669044, 999999999.989595, 2.8907806731461556)]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(anomalies)#materialize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To think of, but not hand in\n",
    "\n",
    "What kinds of anomalies will this algorithm pick up? What kinds would a shorter \"window\" of anomaly detection, like 100 points around the time in question pick? How might you create an algorithm which does window based averaging? (hint: the window size is small compared to the time series size). \n",
    "\n",
    "Finally think a bit of how you might implement all of this in a production environment..remember that data streaming in might get backed up when you handle an anomaly.\n",
    "\n",
    "(Some inspiration might accrue if you look at the docs for `collections.deque`)."
   ]
  }
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